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Diophantine geometry, is the application of techniques from algebraic geometry which considers equations that also have a geometric meaning. The central idea of Diophantine geometry is that of a rational point , namely a solution to a polynomial equation or a system of polynomial equations , which is a vector in a prescribed field K , when K is ...
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer .
The equation given by Fuss' theorem, giving the relation among the radius of a bicentric quadrilateral's inscribed circle, the radius of its circumscribed circle, and the distance between the centers of those circles, can be expressed as a quadratic equation for which the distance between the two circles' centers in terms of their radii is one ...
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a , b , c , and d of the cubic equation are real numbers , then it has at least one real root (this is true for all odd-degree polynomial functions ).
In classical algebraic geometry, the genus–degree formula relates the degree of an irreducible plane curve with its arithmetic genus via the formula: = (). Here "plane curve" means that is a closed curve in the projective plane.
septic equation for degree seven; octic equation for degree eight; A Diophantine equation is an equation where the unknowns are required to be integers; A transcendental equation is an equation involving a transcendental function of its unknowns; A parametric equation is an equation in which the solutions for the variables are expressed as ...
Conversely, every maximal continuously differentiable solution of this partial differentiable equation is a positively homogeneous function of degree k, defined on a positive cone (here, maximal means that the solution cannot be prolongated to a function with a larger domain).